Question

Determine the remainder when (5x3 + 49x2 + 74x + 6) is divided by (x + 8).

Answer 1

The polynomial remainder theorem says that the remainder when dividing a polynomial $P(x)$ by a linear divisor $x-k$ is simply $P(k)$.

If $P(x)=5x^3+49x^2+74x+6$, then the remainder upon dividing by $x+8$ is

$P(-8)=-10$

You could also verify this by actually computing the quotient and remainder.